Problem: Anand knows from experience that if he does not review a new vocabulary word that he has learned, that he has a $70\%$ chance of forgetting it each day. Let $D$ be the number of days Anand goes without reviewing a word until he forgets it. Find the probability that it takes Anand $4$ or more days to forget the word. You may round your answer to the nearest hundredth. $P(D\geq 4)=$
Without a fancy calculator On each day: $P({\text{forget}})=0.7$ $P(\text{remember}})=0.3$ If it takes Anand $4$ or more days to forget the word, then he must remember for each of the first $3$ days. $\begin{aligned} P(D\geq 4)&=P(\text{remember first 3}) \\\\ &=(0.3})^3 \\\\ &= 0.027 \end{aligned}$ $P(D\geq 4) = 0.027 \approx 0.03$